Cam design per VDI 2143
Design motion laws for cam mechanisms per VDI 2143 and check pressure angle, curvature, lift-off and manufacturability right in your browser. The calculator provides motion diagrams and the cam contour.
Cam design calculator
Results
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Formulas and fundamentals
The guideline VDI 2143 describes motion laws for cam mechanisms. The calculator uses the polynomial 4-5-6-7 with the normalized profile s(u) = 35u⁴ − 84u⁵ + 70u⁶ − 20u⁷. At the segment boundaries (u = 0 and u = 1) velocity, acceleration and jerk are zero, so the transitions are C3-continuous and jerk-free.
The pressure angle α describes the force direction between cam and roller: tan α = s′(φ) / (r_base + s). It is evaluated over the full revolution and checked against the configured limit; 30 degrees is a common maximum. In addition the calculator reports the base circle radius required to satisfy the limit.
The radius of curvature of the pitch curve follows from the polar form ρ = (r² + s′²)^(3/2) / |r² + 2s′² − r·s″| with r = r_base + s. If its minimum falls below the roller radius, undercut occurs. The calculator also checks the curvature of the machined contour against cutter radius and safety factor, and the contact force from inertia, spring and preload against lift-off.
Worked example
The default project lifts the follower by 40 mm within 60 degrees, dwells, returns in two segments of 10 mm and 30 mm and dwells until 360 degrees. Base circle radius 130 mm, roller radius 10 mm, speed 60 rpm, mass 2 kg, spring rate 30 N/mm, preload 150 N.
The calculator returns a maximum pressure angle of 29.29 degrees (limit 30 degrees), a minimum pitch curve radius of curvature of 37.70 mm and a resulting safety factor of 3.77 with respect to the roller radius. All six criteria pass; the cam is free of undercut and manufacturable.
Frequently asked questions
What is VDI 2143?
VDI 2143 is a guideline for motion laws in cam mechanisms. It defines normalized transfer functions and their characteristic values for cam design, including polynomial, sinusoidal and trapezoidal laws.
Why is the polynomial 4-5-6-7 jerk-free?
With the polynomial 4-5-6-7 not only velocity and acceleration but also jerk (the third derivative) are zero at both segment boundaries. The motion is C3-continuous, so transitions to dwells produce no jerk peaks and no unnecessary vibration excitation.
Which pressure angle limit should I use?
For translating roller followers a maximum of 30 degrees is common; oscillating levers allow up to about 45 degrees. Larger pressure angles create high lateral forces in the follower guide and can lead to jamming. The calculator checks the maximum over the full revolution against the configured limit.
What is undercut and how do I avoid it?
Undercut occurs when the minimum radius of curvature of the pitch curve is smaller than or equal to the roller radius. The roller can no longer follow the intended path and the contour is distorted. Remedies are a larger base circle, a smaller roller or a gentler motion law with a larger drive angle.
How large does the base circle need to be?
The base circle must be large enough to satisfy the pressure angle limit and the curvature criteria. The calculator reports the required base circle radius for the pressure angle limit: r_base ≥ max(|s′| / tan α_allow − s) over the revolution. In addition the safety factor from radius of curvature and roller radius is checked.
Which export formats are available?
As a Pro feature, a DXF export of the cam contour for CAD and CAM as well as a verification PDF with inputs, characteristic values and criteria are planned. The calculation itself runs entirely in the browser.